A spatial autoregressive stochastic frontier model for panel data with asymmetric efficiency spillovers

Abstract

By blending seminal literature on non-spatial stochastic frontier models with key contributions to spatial econometrics we develop a spatial autoregressive (SAR) stochastic frontier model for panel data. The speci…cation of the SAR frontier allows e¢ ciency to vary over time and across the cross-sections. E¢ ciency is calculated from a composed error structure by assuming a half-normal distribution for ine¢ -ciency. The spatial frontier is estimated using maximum likelihood methods taking into account the endogenous SAR variable. We apply our spatial estimator to an aggregate production frontier for 41 European countries over the period 1990 2011.In the application section, the …tted SAR stochastic frontier speci…cation is used to discuss, among other things, the asymmetry between e¢ ciency spillovers to and from a country.

Measurement and Determinants of Multi‐factor Productivity: A Survey of Literature

“…Glass et al . (2016) develop heteroscedastic version of the spatial autoregressive stochastic frontier for panel data, whose specification allows efficiency to vary over time and across the cross‐sections. Similarly, Greene et al .…”

“…The advantage of SFA 10 over DEA is that it values the possible impact of noise (asymmetric term) on the positioning and shape of the frontier. Glass et al (2016) develop heteroscedastic version of the spatial autoregressive stochastic frontier for panel data, whose specification allows efficiency to vary over time and across the cross-sections. Similarly, Greene et al (2016) provide a discussion on the methods of introducing heterogeneity into the parameters of the stochastic frontier model via fixed and random effects specifications.…”

Bayesian Treatments for Panel Data Stochastic Frontier Models with Time Varying Heterogeneity

“…Following their model specification, the BFES is characterized by marginal prior independence between the individual effects. Therefore, the effects are assumed not to be linked across firms, as would be the case for the spatial stochastic frontier considered by Glass et al (2016). As for measuring the inefficiency, the essence of the Schmidt and Sickles (1984) device in the Bayesian context is that, during the sth of the total S (MCMC) iterations or paths, inefficiency is constructed as the difference of the individual effect from the maximum effect across firms:…”

Endogenous network production functions with selectivity

“…This is in contrast to the spatial production function work of Druska and Horrace (2004) or Glass et al (2014), where the unit of observation is the firm, and exogenous networks are conceptualized as output/input spillovers across firms (or countries) measured as geographic distances or contiguity in a spatial estimation framework, and where consistency arguments are for large numbers of firms (or countries). In these papers it is not easy to conceptualize the network (spillover) mechanism or to argue that the adjacency matrix is the correct 11 There is a large literature that exploits random allocation of individuals into groups to assess the existence of peer effects in other (non-productivity) contexts (e.g., Sacerdote, 2001;Angrist and Lang, 2004;Kling et al, 2007;Chetty et al, 2011;Duflo et al, 2011;Carrell et al, 2013).…”